An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, compressible, perfect-gas flows is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Viscous terms are discretized using central differences. The relaxation strategy is well suited for computers employing either vector or parallel architectures. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. Convergence rates and grid refinement studies are conducted for Mach 5 flow through an inlet with a 10 deg compression ramp and Mach 14 flow over a 15 deg ramp. Predictions for pressure distributions, surface heating, and aerodynamics coefficients compare well with experiment data for Mach 10 flow over a blunt body.

https://ntrs.nasa.gov/api/citations/19900007726/downloads/19900007726.pdf

An upwind-biased, point-implicit relaxation algorithm for viscous, compressible perfect-gas flows

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the eliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high ratio grids.

/pdf/a-psuedo-temporal-multi-grid-relaxation-scheme-for-solving-1xf6z7pt9y.pdf

A Psuedo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

An upwind-biased point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional viscous hypersonic flows in chemical and thermal nonequilibrium is described. Details of the algorithm development, in the context of an 11-species two-temperature reacting gas model, are emphasized. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large block-tridiagonal systems. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km) over the Aeroassist Flight Experiment configuration, obtained on a multidomain grid, are discussed.

Upwind-biased, point-implicit relaxation strategies for viscous, hypersonic flows

A new computer code for the solution of the three-dimensional parabolized Navier-Stokes equations has been developed. The code employs a state-of-the-art upwind algorithm to capture strong shock waves. The algorithm is implicit, uses finite volumes, and is second-order accurate in the crossflow directions. The new code is validated through application to laminar hypersonic flows past two simple body shapes: a circular cone of 10 deg half-angle, and a generic all-body hypersonic vehicle. Cone flow solutions were computed at angles of attack of 12, 20, and 24 deg and results are in agreement with experimental data. Results are also presented for the flow past the all-body vehicle at angles of incidence of 0 and 10 deg.

Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

Practical applications of new LU-ADI scheme for the three-dimensional Navier-Stokes computation of transonic viscous flows

Multi-dimensional formulation of CSCM - An upwind flux difference eigenvector split method for the compressible Navier-Stokes equations

/pdf/universal-single-level-implicit-algorithm-for-gasdynamics-3p75reyt0i.pdf

Universal single level implicit algorithm for gasdynamics

Preliminary investigations have led to the consideration of two classes of energy efficient aeroassisted orbital transfer vehicle (AOTV) concepts, with high and low L/D. The AOTV represent reentry space vehicles which are to fly hypersonically in the continuum upper reaches of the atmosphere. Problems arise in connection with convective and nonequilibrium radiative heating. As the possibilities for obtaining needed information by experimentation are limited, reliance must be placed on computational techniques to simulate testing of design concepts. A new relaxation algorithm for the compressible Navier-Stokes equations has been developed in the context of recent work with a conservative flux difference eigenvector split implicit upwind scheme CSCM (conservative supracharacteristics method). Attention is given to the CSCM implicit method, and early results for axisymmetric bluff body flow including complete forebody and base flow for a free flight range model drag brake AOTV.

AOTV bluff body flow - Relaxation algorithm

The single level conservative supra characteristic method (CSCM-S) is an upwind implicit method that is very robust and in a single level relaxation format makes efficient use of computer resources, and is very rapidly convergent. These factors render the unconditionally stable algorithm a useful compromise between Parabolized Navier-Stokes methods and two level linearized implicit time dependent methods and, thus, the method is very attractive for multidimensional Navier-Stokes problems. In this paper the heat transfer prediction capabilities of the CSCM schemes for flat plate, nozzle, blunt cone and bluff body flows are reported for the first time. Results are compared with available experimental heat transfer measurements.

Two Dimensional and Axisymmetric Heat-Transfer Results with the CSCM Upwind Implicit Algorithm

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Multi-dimensional formulation of CSCM - An upwind flux difference eigenvector split method for the compressible Navier-Stokes equations

Universal single level implicit algorithm for gasdynamics

AOTV bluff body flow - Relaxation algorithm

Two Dimensional and Axisymmetric Heat-Transfer Results with the CSCM Upwind Implicit Algorithm